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arXiv · 2507.05634

A Note on Inferential Decisions, Errors and Path-Dependency

Kangda K. Wren
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Abstract

Consider the sequential inference of a binary outcome. The process of a posteriori beliefs and its objective conditional probability counterpart generally differ but converge to the same result in well-defined outcome-resolving tests. We show that unless the two processes are 'essentially identical', differing only by a priori factors, time-homogeneous continuous decisions based on one must fail to be path-independent with respect to state-variables based on the other, or any non-essentially-identical processes. Inferential error decomposes into a path-independent and a path-dependent component, whose distinct properties are relevant to error mitigation.

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Kangda K. Wren. 2025-07-08. A Note on Inferential Decisions, Errors and Path-Dependency. https://arxiv.org/abs/2507.05634

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